Elementary operations for the reorganization of minimally persistent formations
(2006) MTNS 2006 — Location: Kyoto, Japan
Files
06HFYAB.pdf
Restricted Access - Adobe PDF
- 167.6 KB
Details
- Authors
- Abstract
- In this paper we study the construction and transformation of two-dimensional minimally persistent graphs. Persistence is a generalization to directed graphs of the undirected notion of rigidity. In the context of moving autonomous agent formations, persistence charac- terizes the efficacy of a directed structure of unilateral distances constraints seeking to preserve a formation shape. Analogously to the powerful results about Henneberg sequences in minimal rigidity theory, we propose different types of directed graph operations allowing one to sequen- tially build any minimally persistent graph (i.e. persistent graph with a minimal number of edges for a given number of vertices), each intermediate graph being also minimally persistent. We also consider the more generic problem of obtaining one minimally persistent graph from another, which corresponds to the on-line reorganization of an autonomous agent formation. We show that we can obtain any minimally persistent formation from any other one by a se- quence of elementary local operations such that minimal persistence is preserved throughout the reorganization process.
- Affiliations
Australian National University RSISE
Citations
Hendrickx, J., Fidan, B., Yu, C., Anderson, B. D. O., & Blondel, V. (2006). Elementary operations for the reorganization of minimally persistent formations. Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems. Published. MTNS 2006, Kyoto, Japan. https://hdl.handle.net/2078.5/225587